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Deriving the autocovariances of powers of Markov-switching GARCH models, with applications to statistical inference

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  • Francq, Christian
  • ZakoI¨an, Jean-Michel

Abstract

A procedure is proposed for computing the autocovariances and the ARMA representations of the squares, and higher-order powers, of Markov-switching GARCH models. It is shown that many interesting subclasses of the general model can be discriminated in view of their autocovariance structures. Explicit derivation of the autocovariances allows for parameter estimation in the general model, via a GMM procedure. It can also be used to determine how many ARMA representations are needed to identify the Markov-switching GARCH parameters. A Monte Carlo study and an application to the Standard & Poor index are presented.

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  • Francq, Christian & ZakoI¨an, Jean-Michel, 2008. "Deriving the autocovariances of powers of Markov-switching GARCH models, with applications to statistical inference," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 3027-3046, February.
  • Handle: RePEc:eee:csdana:v:52:y:2008:i:6:p:3027-3046
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    7. DUFAYS, Arnaud, 2012. "Infinite-state Markov-switching for dynamic volatility and correlation models," LIDAM Discussion Papers CORE 2012043, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    11. Aknouche, Abdelhakim & Demmouche, Nacer, 2019. "Ergodicity conditions for a double mixed Poisson autoregression," Statistics & Probability Letters, Elsevier, vol. 147(C), pages 6-11.
    12. CARPANTIER, Jean-François & DUFAYS, Arnaud, 2014. "Specific Markov-switching behaviour for ARMA parameters," LIDAM Discussion Papers CORE 2014014, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    13. Aknouche, Abdelhakim & Demouche, Nacer, 2018. "Ergodicity conditions for a double mixed Poisson autoregression," MPRA Paper 88843, University Library of Munich, Germany.
    14. Carol Alexander & Emese Lazar, 2009. "Modelling Regime‐Specific Stock Price Volatility," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(6), pages 761-797, December.
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    21. Pérez, Ana & Ruiz, Esther & Veiga, Helena, 2009. "A note on the properties of power-transformed returns in long-memory stochastic volatility models with leverage effect," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3593-3600, August.
    22. Wee, Damien C.H. & Chen, Feng & Dunsmuir, William T.M., 2022. "Likelihood inference for Markov switching GARCH(1,1) models using sequential Monte Carlo," Econometrics and Statistics, Elsevier, vol. 21(C), pages 50-68.
    23. Pappas, Vasileios & Ingham, Hilary & Izzeldin, Marwan & Steele, Gerry, 2016. "Will the crisis “tear us apart”? Evidence from the EU," International Review of Financial Analysis, Elsevier, vol. 46(C), pages 346-360.

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